Ion coordination and migration mechanisms in alkali metal complex borohydride-based solid electrolytes

Description of the M₂B₁₂H₁₂ structure and suitable computational approach

The two prime structural descriptors of the M₂B₁₂H₁₂ molecular solids, namely, the global lattice description of the crystal through symmetry and the local structure defined by the coordination environment of cations, are depicted in Fig. 1. The crystal structures of room temperature phases of M₂B₁₂H₁₂ (M = Li, Na, K) consist of metal cations (M⁺) and framework anion (FA: \({{{\rm{B}}}}_{12}{{{\rm{H}}}}_{12}^{2-}\)), interacting through local M–H bonds, as shown in Fig. 1a–c. The nature of M–H interaction dictates the local coordination sphere (LCS) of M⁺, which transitions from a triangular equatorial plane to distorted tetrahedra and eventually to perfect tetrahedra as the M changes from Li to Na to K (Fig. 1d–f). The collective arrangement of these local units determines the overall structural symmetry of the M₂B₁₂H₁₂ crystal structures, which shifts from Pa\(\overline{3}\) in Li₂B₁₂H₁₂ to P2₁/c in Na₂B₁₂H₁₂ and finally to Fm\(\overline{3}\) in K₂B₁₂H₁₂ (Fig. 1a–c)^52,53,54.

Optimized crystal structure and local cation coordination environment for a, d Li₂B₁₂H₁₂ (ICSD-249756), b, e Na₂B₁₂H₁₂ (ICSD-164649), and c, f K₂B₁₂H₁₂ (ICSD-98616), with PBEsol functional. The M–H bond distances in the first coordination spheres are highlighted with a single bond type (p) for Li and K and a doublet consisting of p₁ and p₂ types for Na. g The volume per atom of the optimized structures of Li₂B₁₂H₁₂ (maroon pentagons) and Na₂B₁₂H₁₂ (yellow squares) was calculated with various density functional approximations. Dashed lines indicate the experimental references. h Radial distribution function, g(r), for Na–H pair in Na₂B₁₂H₁₂. The peak p₁ corresponds to shorter Na–H bonds, whereas peak p₂ is indicative for the out-of-plane shift of Na from planar triangular coordination. The blue and pink shades in the plot signify the range of p₁ and p₂ peaks. i The change in volume as a function of the packing efficiency factor, which is calculated by summing the cube of ionic radii (\(2{{R}}^{3}_{C}+{{R}}^{3}_{A}\)), demonstrates a deviation from linearity.

To account for the superionic diffusion properties of these structures, deep insight into events of long-range cation hoping is required, which necessitates an accurate method for predicting both the crystal volume and LCS. Hence, the suitability of exchange-correlation functionals is assessed to determine the accurate method for predicting the M₂B₁₂H₁₂ structures, ranging from generalized gradient approximation (GGA) to advanced hybrid functionals such as Perdew–Burke–Ernzerhof (PBE), revised PBE for solids (PBEsol), and Heyd–Scuseria–Ernzerhof (HSE), coupled with dispersion-correction schemes like non-local many-body dispersion (MBDNL) and the pairwise Tkatchenko–Scheffler (TS) scheme. Additionally, lattice expansion under quasi-harmonic approximation (QHA) was computed to obtain accurate volume at room temperature. The pairwise approximation to account for dispersion interaction (PBE-TS and HSE-TS) tends to underestimate the volume, while without dispersion correction (PBE and HSE) slightly overestimate it. Incorporating the effects of thermal expansion with QHA increases the disparities between experimental data and volume estimates obtained using PBE (see PBE-QHA results in Fig. 1g), and a similar trend is expected for HSE functional. In contrast, the PBEsol-QHA approach demonstrates excellent accuracy in predicting lattice expansion at 300 K (Fig. 1g). Overall, the comparative analysis reveals that PBEsol functional provides results in good agreement with experimental references^52,53,54.

To gain insight into LCS, the radial distribution function (RDF) for the M–H pair is computed (Figs. 1h, S1a, b). Especially, the first LCS of Na⁺ in Na₂B₁₂H₁₂ exhibits an intrinsic heterogeneity, manifested by two distinct ranges of Na–H bond distances, identified as the p₁ and p₂ peaks in Fig. 1e. The significant distortion in the local structure of Na₂B₁₂H₁₂ emphasizes the need to determine the placement of Na in the distorted tetrahedra configuration accurately. It is found that the LCS (Fig. 1d–f) is accurately described by HSE-MBDNL, PBE-MBDNL, and PBEsol, with the shoulder peak (p₂ in Fig. 1h) precisely predicted. In contrast, without consideration of dispersion interaction fails to describe the LCS accurately. Thus, these findings highlight the importance of long-range exchange correlation and non-local many-body dispersion in characterizing the local structure within the M₂B₁₂H₁₂ class of SEs. The average number of hydrogen coordinating with M-cation in its first coordination sphere is shown in Fig. S1e, showing 6, 9, and 12 coordination for Li₂B₁₂H₁₂, Na₂B₁₂H₁₂, and K₂B₁₂H₁₂, respectively, which is in accordance with experimental findings⁵³. Accordingly, the preceding results discussed in this study have been obtained using the suitable density functional approximation (PBEsol) and an appropriate description of dispersion interactions through the MBDNL scheme (HSE-MBDNL).

The extent of out-of-plane positioning of M-ion from the triangular plane of borohydride moieties increases while moving from Li to Na to K. In literature, such trends are generally rationalized using the cation/anion radius ratio (R_C/R_A) rule⁵⁵. As R_C/R_A increases, the coordination number of cations increases such that minimum theoretical limits for R_C/R_A are 0.155, 0.225, and 0.414 for trigonal, tetrahedral, and octahedral site occupation, respectively. According to Shannon ionic radii trends, R_C decreases from K⁺ (1.64 Å) to Na⁺ (1.24 Å) to Li⁺ (0.76 Å)⁵⁶. The B–B and B–H bonds remain the same in the presence of different M⁺ cations (Fig. S1c, d). The computed anionic radius (R_A) for \({{{\rm{B}}}}_{12}{{{\rm{H}}}}_{12}^{2-}\) moiety is 2.90 Å. The larger size of K⁺ leads to R_C/R_A = 0.56, which contradicts the observed perfect tetrahedral arrangement of K⁺ in K₂B₁₂H₁₂. A similar contradiction is observed for Li and Na, which have R_C/R_A of 0.26 and 0.42, respectively, highlighting the importance of polarization to dictate the M₂B₁₂H₁₂ structure.

Notably, the volume of M₂B₁₂H₁₂ expands gradually from Li to Na to K. However, this progression deviates from the expected linear correlation between the volume and packing efficiency factor (Fig. 1i and Table 1), which is defined as the sum of the cube of constituent ionic radii (\(2{R}_{{\rm {C}}}^{3}+{R}_{{\rm {A}}}^{3}\), see “Methods” section). Overall, the packing efficiency (Eq. (1)) refers to the percentage of space occupied by atoms in a structure. The K₂B₁₂H₁₂ framework exhibits sufficient spacing between \({{{\rm{B}}}}_{12}{{{\rm{H}}}}_{12}^{2-}\) anions to achieve Fm\(\overline{3}\) packing. The smallest-sized Li⁺ perfectly fits in the triangular equatorial plane, contributing to the slightly denser packing in Li₂B₁₂H₁₂ compared to its Na and K analogs (Table 1). In contrast, the intermediate-sized Na+ ions necessitate a significantly distorted local structure, as also reflected in the overall symmetry reduction in the Na₂B₁₂H₁₂ framework (P21/c), resulting in a non-monotonous behavior in the series.

Thus, the higher packing efficiency of Li₂B₁₂H₁₂ indicates the lesser void spaces within the framework. Notably, despite the notable differences in the ratio of cation to anion radii (R_C/R_A) for Na₂B₁₂H₁₂ (0.42) and K₂B₁₂H₁₂ (0.56), both exhibit similar packing efficiency (46%) (Table 1). Thus, the radius-ratio rule that solely accounts for electrostatics operating within the system, fails to predict both local structure and packing efficiency trends of M₂B₁₂H₁₂ class of molecular solids.

Nature of chemical bonding within M₂B₁₂H₁₂ framework

The electron localization function (ELF) analysis on 3D-M₂B₁₂H₁₂ framework (Fig. 2a–c) reveals a strong polar covalent nature of the \({{{\rm{B}}}}_{12}{{{\rm{H}}}}_{12}^{2-}\) cage while the interaction between M and H exhibits negligible covalent character (see Fig. S3c, e, g for isolated M₂B₁₂H₁₂). As shown in Fig. 2d–f, differential charge density (DCD) plots reveal the positively charged boron core and negatively charged hydrogen shell within the \({{{\rm{B}}}}_{12}{{{\rm{H}}}}_{12}^{2-}\) moiety (see Fig. S3d, f, h for isolated M₂B₁₂H₁₂). The bader charge over each cation and \({{{\rm{B}}}}_{12}{{{\rm{H}}}}_{12}^{2-}\) cage is presented in Table S1. Since the \({{{\rm{B}}}}_{12}{{{\rm{H}}}}_{12}^{2-}\) anion lacks localized charge, the compensation of M⁺ charges requires non-local, long-range interactions. Indeed, the noncovalent interaction (NCI) isosurface plots (Fig. 2g–i), derived from the non-local many-body dispersion (MBD) interaction, emphasize the prevalence of long-range dispersion interactions within the M₂B₁₂H₁₂ frameworks. However, the nature of NCI gets significantly tuned across the series from Li to Na to K (Fig. 2j–l). Similarly, in MCB₁₁H₁₂ class, the nature of electrostatic and covalent interactions shows minimal variation across the M = Li, Na, and K analogs (Fig. S4a, b). However, the nature of dispersion interactions displays significant differences among these M-ion analogs (Fig. S4c), a trend that holds true for both the M₂B₁₂H₁₂ and MCB₁₁H₁₂ classes.

Electron localization function (iso value = 0.8) and differential charge density (iso level = 0.02 e Bohr⁻³) in a, d Li₂B₁₂H₁₂, b, e Na₂B₁₂H₁₂, and c, f K₂B₁₂H₁₂. The red (blue) isosurface in differential charge density plots corresponds to the charge density accumulation (depletion). Non-covalent interaction (NCI) plots (s = 0.4 a.u.) showing total and cation-anion interactions in g, j Li₂B₁₂H₁₂, h, k Na₂B₁₂H₁₂, and i, l K₂B₁₂H₁₂. The isosurfaces are color-coded on a blue-green-red scale based on the values of sign (λ₂) ⋅ ρ, ranging from  −0.025 to  +0.025 a.u. Blue and red represent intense attractive overlaps and non-bonded (repulsive) interactions, respectively.

Particularly, the MBD interaction in Li₂B₁₂H₁₂ predominantly exists between framework moieties (FA–FA). On the contrary, in K₂B₁₂H₁₂, the primary dispersion interaction occurs between the cation and the framework (K–FA). Na₂B₁₂H₁₂ showcases an intermediate scenario, where both the Na–FA and FA–FA NCI are moderately weak, resulting in an overall reduction in MBD interactions (E_{disp,periodic}) within the framework (Table 1) while comparing with Li and K analogs (Li₂B₁₂H₁₂: −3.05 eV/f.u.; Na₂B₁₂H₁₂: −2.83 eV/f.u.; K₂B₁₂H₁₂: −3.33 eV/f.u.). In contrast, while examining molecular M₂B₁₂H₁₂ moieties, there is a systematic rise in non-covalent energy as atom size increases (Li₂B₁₂H₁₂: −1.78 eV/f.u.; Na₂B₁₂H₁₂: −1.83 eV/f.u.; K₂B₁₂H₁₂: −2.03 eV/f.u.). The 3D Na₂B₁₂H₁₂ framework displays weaker non-covalent stability compared to Li₂B₁₂H₁₂, diverging from the anticipated trend found in the case of isolated molecular moieties.

The overall stability upon the formation of 3D solid frameworks from the aggregation of isolated molecular entities is evaluated using ΔE_tot,pack. ΔE_tot,pack quantifies the energy difference between solid-state and isolated molecular configurations of M₂B₁₂H₁₂, as outlined in Table 1. Notably, an upward trend in ΔE_tot,pack is demonstrated with the variation of M from Li (−3.13 eV/f.u.) to Na (−3.42  eV/f.u.) to K (−3.93 eV/f.u.). Interestingly, dispersion energy per formula unit in M₂B₁₂H₁₂ molecular solids (E_{disp,periodic}) follows a non-linear trend: (Li₂B₁₂H₁₂: −1.27 eV/f.u.; Na₂B₁₂H₁₂: −1.02 eV/f.u.; K₂B₁₂H₁₂: −1.29 eV/f.u.). Upon further quantitative analysis, when ΔE_tot,pack is deconstructed into two distinct categories—stability influenced by electrostatic and covalent interactions, and stability driven by non-covalent interactions (ΔE_disp,pack)–it becomes apparent that ΔE_disp,pack significantly contributes to ΔE_tot,pack (δE_disp ≈ 30–40%) during the process of molecular packing (Table 1), highlighting the role of MBD interactions within these ionic frameworks. The highest δE_disp of 40% is obtained for Li₂B₁₂H₁₂ due to strong FA–FA interaction. In contrast, strong M–FA interaction leads to the 33% δE_disp in K₂B₁₂H₁₂. Na₂B₁₂H₁₂ exhibits the least δE_disp (30%) in the series, due to the fact that neither the FA–FA nor the M–FA interaction is as strong as the case of Li₂B₁₂H₁₂ and K₂B₁₂H₁₂, respectively. This disparity highlights the complex and non-local characteristics of dispersion interactions within the M₂B₁₂H₁₂ frameworks, leading to diverse properties within the same class while varying M.

Metal ion diffusion within M₂B₁₂H₁₂ framework

The distinctive arrangement of the M sublattice within the M₂B₁₂H₁₂ structure signifies the varied chemical environments experienced by M as it shifts from Li to Na to K (Fig. 3a–c). The subsequent objective is to identify minimum energy pathways (MEPs) that facilitate long-range cation diffusion in the periodic M₂B₁₂H₁₂ (M = Li, Na, K) SSEs. All the Li ions are arranged in a parallelepiped-type shape with equal edges (Fig. 3a) in Li₂B₁₂H₁₂ that results in three geometrically unique Li migration paths (L1, L2, and L3) within a migration path length of 7 Å. Path L1 involves hopping along the body diagonal, path L2 involves hopping along the edges, and path L3 involves hopping across the faces of the parallelepiped Li-structure. Our calculations show that facial hopping (L3 path) is the most energetically demanding hop, whereas edge (L2 path) and body-diagonal (L1 path) hopping are favorable (Fig. 3d). We note that, the combination of L1 and L2 hopping leads to a long-range three-dimensional Li⁺ diffusion within the Li₂B₁₂H₁₂ framework, associated with a considerably low E_a of ≈300 meV.

Possible hopping paths are shown for a Li₂B₁₂H₁₂ with L1: body diagonal, L2: edge, L3: face diagonal of a parallelepiped 3D arrangement of Li sublattices. b Na₂B₁₂H₁₂ with in-plane (N2, N3, N6) and out-of-plane (N1, N4, N6) connections in distorted hexagonal close packing of Na sublattices. c K₂B₁₂H₁₂ with K1: edge, K2: face diagonal, K3: body diagonal of a cubic arrangement of K sublattices. Relative migration barrier (ΔE) as a function of the reaction coordinate for d Li, e Na, and f K cation within respective M₂B₁₂H₁₂ framework. Path lengths (d) corresponding to each migration path are shown by right-side color bar. g Li, Na, and K hopping in respective isolated M₂B₁₂H₁₂ molecules along the migration path (A → B → C → D  → E) shown on the right side. The dotted line for M = K (while solid lines for M = Li and Na) in this plot is for visual clarity due to the merged lines for Na and K analogs.

The eight Na ions in Na₂B₁₂H₁₂ (Fig. 3b) are arranged in the distorted hexagonal close packing that results in six distinct paths (N1–N6) within a migration path length of 7 Å. Path N3 and N6 lead to in-plane (along ac direction) edge hopping, path N2 results in in-plane diagonal hopping, whereas paths N1, N4, and N5 correspond to out-of-plane diagonal hopping. Na⁺ migration along N4 (E_a = 412 meV) is the MEP (Fig. 3e). For the execution of long-range three-dimensional migration Na⁺ in Na₂B₁₂H₁₂ with the least possible E_a, a combination of the N6 and N3 path (in-plane; E_a ≈ 500 meV) and N4 (out-of-plane; E_a = 412 meV) is needed. Hence, unlike Li₂B₁₂H₁₂, there are constraints for direct Na⁺ in-plane hopping, acting as a diffusion-limiting step with E_a of  ≈500 meV.

The eight K ions (Fig. 3c) are arranged in perfect cubic shape in K₂B₁₂H₁₂. It has three distinct migration paths within a migration path length of 10 Å, and these paths can be classified into three types: edge (K1), facial (K2), and body-diagonal hopping (K3) with K2 being the MEP (Fig. 3f). The combination of K2 and K3 (E_a > 700 meV) lead to long-range K⁺ diffusion. In contrast to Li₂B₁₂H₁₂ and Na₂B₁₂H₁₂, K₂B₁₂H₁₂ exhibits significant activation barriers in all three dimensions, although it has a packing efficiency lower than Li analog and comparable to its Na analogs (as detailed in Table 1). Consequently, instead of focusing solely on free volume and overall structure, it becomes imperative to understand the local coordination environment of the migrating ion within this class.

For isolated M₂B₁₂H₁₂, we have considered five M⁺-hopping steps around the \({{{\rm{B}}}}_{12}{{{\rm{H}}}}_{12}^{2-}\) spherical cage, each occurring at an angle of 36° (migration path: A → B → C → D → E in right panel of Fig. 3g). The migration barriers (E_a) for each hopping step are 254 meV for Li, 209 meV for Na, and 211 meV for K, as shown in Fig. 3g which are in corroboration with previous study by Kweon et al.⁵⁵. It is evident that the E_a increase when the molecular moieties are packed into molecular solids (Fig. 3d–f). Notably, this rise in E_a for Li is relatively small compared to the significant increase found in Na and K analogs.

Impact of local structure and dispersion interaction on metal ion migration barrier

We have identified a variation in the dispersion interaction (ΔE_disp) as the M ion migrates along the diffusion paths, from the initial state (IS) to the final state (FS) via transition states (TS) and intermediate states (INTs), within the M₂B₁₂H₁₂ framework in both molecular and solid-state diffusion (Fig. 4). Despite this variation, the formal charges of M remain nearly constant throughout the diffusion coordinates (Fig. S2), suggesting that electronic polarization effect plays a key role in regulating M migration within the M₂B₁₂H₁₂ framework.

Relative energy (ΔE) and relative many-body dispersion energy (ΔE_disp) with respect to the initial state (IS), as a function of the reaction coordinates along the minimum energy migration path in a 3D-Li₂B₁₂H₁₂; b 3D-Na₂B₁₂H₁₂; c 3D-K₂B₁₂H₁₂; and d isolated M₂B₁₂H₁₂ molecules (M = Li, Na, and K). Green diamond symbols corresponds to ΔE_disp. The migration path (A → B → C → D → E) for isolated M₂B₁₂H₁₂ is shown in Fig. 3g.

In M₂B₁₂H₁₂ molecular solids, stable sites (IS, FS) experience varying degrees of stabilization from MBD interaction compared to the TS and INTs, as detailed in Fig. 4a–c. Notably, the MBD-driven stability of IS and FS is greater than that of TS or INTs for Na₂B₁₂H₁₂ and K₂B₁₂H₁₂, while Li₂B₁₂H₁₂ exhibits the opposite behavior. In contrast, for the isolated M₂B₁₂H₁₂ molecular moieties, MBD-driven stability of IS and FS is always greater than the TS, irrespective of the M ions (Fig. 4d). The impact of molecular packing on the tunable energetics of the diffusion coordinates is further understood by analyzing the local structure of IS/FS and TS/INTs in the subsequent section.

The local coordination sphere (LCS) evolves as M-ion progresses through the diffusion coordinates within the M₂B₁₂H₁₂ framework. We introduce the effective coordination number (ECN) to describe the LCS of M surrounded by B₁₂H₁₂ moieties. ECN is defined as the effective number of (nearest) hydrides surrounding the M⁺ cation at different configurations (IS, TS, INTs, FS, etc.) along the diffusion path. Mathematically, ECN =\(\frac{{r}_{{\rm {IS}}}}{{r}_{{\rm {cut}}}}\times N({r}_{{\rm {cut}}})\), where r_IS is the least M–H distance in IS; r_cut is the cutoff radius to define the first-coordination sphere; and N(r_cut) is the number of hydrides surrounding the M⁺ cation within the cutoff r_cut. The cutoff distance (r_cut) that defines the LCS is specific to the M-ion within the framework. r_cut represents the minimum radius ensuring M at the core and allowing us to describe the first coordination sphere for all configurations during the migration process, including IS, FS, TS, and INTs (Fig. S1f–h). For example, while Li exhibits a highly symmetric trigonal planar arrangement in the IS, it adopts a tetrahedral geometry in the TS. A minimum distance cut-off of 2.9 Å adequately captures both trigonal planar and tetrahedral environments assumed by Li during the migration process. Similarly, the r_cut is 4.5 and 4.2 Å for Na and K, respectively. Slightly higher r_cut for Na compared to K is due to its distorted LCS, while the latter exhibits a highly symmetric LCS. These values of r_cut satisfy the criteria: r_cut ≥ r_vdW, where r_vdW is the combined van der Walls radii of the respective M–H bonds (r_vdW: 2.9, 3.4, and 3.9 Å, for Li–H, Na–H and K–H bonds, respectively). The number of M–H bonds up to the distance r_cut dictates the valus of ECN. For stable M sites, ECN varies from 6 to 9–12, for Li, Na, and K, respectively, while 6 M–H bonds stem from three B₁₂H₁₂ units at triangular planar geometry (2 H from each unit) for Li₂B₁₂H₁₂, four B₁₂H₁₂ units in distorted tetrahedra arrangement (2–3 H atoms from each unit) for Na₂B₁₂H₁₂ and four B₁₂H₁₂ units in perfect tetrahedra arrangement (3H atoms from each unit) for K₂B₁₂H₁₂ (Fig. S1e).

Figure 5 provides an analysis of LCS and MBD-driven stability across IS-TS-FS, along the minimum energy diffusion path within 3D M₂B₁₂H₁₂ frameworks. In Li₂B₁₂H₁₂, the diffusion of Li occurs with ΔECN ≥ 0 (ΔECN = ECN(TS)−ECN(IS)), resulting in either higher MBD-driven stabilization or the maintenance at nearly the same level, across the migration path. As a result, there is no significant net instability of the TS caused by MBD interaction or polarization in a broader sense. In contrast, ΔECN ≤ 0 as progressing through the migration path for Na and K analogs, results in the instability of the TS compared to the IS and enhances the migration barrier. Thus, the MBD interactions impact the total migration barrier differently for each element: it decreases by as much as 9% for Li but increases by 18.1% for Na and 22.8% for K (Fig. 5).

Percentage contribution of relative MBD energy (ΔE_disp) to the total migration barrier (ΔE) as a function of the reaction coordinates for a Li₂B₁₂H₁₂, b Na₂B₁₂H₁₂, and c K₂B₁₂H₁₂. MBD interactions between cation (M⁺) and \({{{\rm{B}}}}_{12}{{{\rm{H}}}}_{12}^{2-}\)(FA) moiety are shown with gradient iso-surface plots (insets, s = 0.5). Number of hydrides, N(r), surrounding cation (M = Li, Na, K) within the first coordination shell (defined as effective coordination number, ECN) is shown in the right panel. The isosurfaces are color-coded on a blue-green-red scale based on the values of sign(λ₂) ⋅ ρ, ranging from  −0.025 to  +0.025 a.u. Blue and red represent intense attractive interactions and non-bonded (repulsive) overlaps, respectively.

Linear correlation between effective coordination number (ECN) and dispersion-driven stabilization

A linear relationship emerges between dispersion-driven stability (E_disp) and ECN, regardless of the M ions in 3D-M₂B₁₂H₁₂, as shown in Fig. 6a. Notably, MBD interaction enhances the stabilization of the configuration with higher ECN and vice versa (Fig. 6b).

a MBD interaction (E_disp) as a function of the effective coordination number (ECN) and b relative dispersion energy (ΔE_disp) as a function of change in effective coordination number (ΔECN) while tracking the reaction coordinates along the minimum energy migration path for M₂B₁₂H₁₂ family with following color codes: Li₂B₁₂H₁₂ (red), Na₂B₁₂H₁₂ (yellow), and K₂B₁₂H₁₂ (magenta).

For M-ion hopping within isolated molecular M₂B₁₂H₁₂ units, ECN(IS) = 3 for all M. However, the ECN at the transition state, ECN(TS), varies slightly, decreasing from Li (2.16) to Na (2.14) to K (2.11), as detailed in Fig S3a. Thus, for molecular M₂B₁₂H₁₂ moieties, ECN follows a systematic decrease in its value during the evolution from IS to TS, irrespective of the M atoms present in the framework. Consequently, MBD stabilizes the IS/FS (ECN =  3) to a higher extent than the TS (ECN ≈ 2) (Fig. S3b). Such reduction in ECN results in MBD-driven instability in the TS compared to those in the IS/FS, irrespective of the nature of the M atom. Hence, MBD interaction always causes retardation in the molecular hopping process in isolated M₂B₁₂H₁₂ moieties. Notably, a small variation in ECN(TS) occurs at the cost of significant alteration in ΔE_disp, as revealed in the high slope (388 meV/ECN) of the ΔE_disp versus ECN plot for isolated M₂B₁₂H₁₂ molecular moieties (Fig. S3b). This indicates a higher sensitivity of ECN on ΔE_disp), reflecting the robust LCS during the isolated molecular hopping process. In contrast, the 3D-M₂B₁₂H₁₂ exhibit a wide range of ECN due to the accessibility of various M-FA LCS during the migration process (Fig. 6b), with a comparatively lower penalty stemming from the MBD-driven instability upon reducing the ECN (22 meV/ECN).